Privatesectorfundingfortheconstructionandoperationoftollroads deRus,GinesandTrujillo,LourdesandRomero,Manuel MunichPersonalRePEcArchive

(1)

Munich Personal RePEc Archive

Private sector funding for the

construction and operation of toll roads

de Rus, Gines and Trujillo, Lourdes and Romero, Manuel

Universidad de Las Palmas de Gran Canaria

2000

Online at https://mpra.ub.uni-muenchen.de/12204/

MPRA Paper No. 12204, posted 16 Dec 2008 14:27 UTC

(2)

!"#"# $ % "$ !"$

(3)

! " #

" $ " " " %

" &

" '

( ) " # $ " " "

( * +

( " * + , # %

( ( " + * -

( % " + "

% " " . '

% / # " " " . 0

% " " # . ((

& # 1 " " (&

& ) " " (&

& 2 " (3

- 4 5 " " " # %

- # " " # " %

- * " " # " . %%

- ( " + 6 " 2 " ! %-

' %3

3 $ &(

0 4 7 %3

(4)

&' ($$"%

7 " " " " 1 *

" " $ " + 4 8 "

* + 9 " " #

$ " " : # # 9 " 7 "

$ "

" " " " 5$ : 7 "

+ : 1 * " * # " " * $

" : 9 * 8 $ " 1 + +

: " # 1 " " 7" " "

" : " " " 5$ : $

1 " * * $ " " ; 1:

: # < " 1

7 " " = $ " " " "

$

" " " :

# : # $ :

" " 8 " 1 1 7 " 1 > "

" , # " " " * : >*

: " " # #

>* " " 8 " " )

* : " # " " 8 8 "

" : " " >*

" # * " " + " 8 "

$ # : # "

>* : * 8 " # 1 7 " #

$ # " * " : "

$ # * : " 8 8

" " " : * :

$ #

# " $ : " 1 1 7 "

" : 9 + 8 * 9 " #

8 * >* * " + 5 " /

& % ? # " " 7 " " : ((

" "5 " # ; 8 $ 8 "

7 " " " " : 1 8 '( " ? # "

>*

4 8 " " " 5$ * :

" 7 " " " * 8 7 " : : *

" 1 " " , " * > " "

" " .

(5)

( &'&' !" " $"% ! # # )"!" ! $ # ( $

$"#"%

! *"#"% # ($$"% " $" $"% + ! $"%

,

- !

(#( "

>* @ >* >* 2

>* )

>* @ >* >* )

>* 2

@ " # * " " : 8 8 "

>* " #

# : # " 1 *

. : A !" + 1 " , # "

; . : : "5 ':& " " "

+ : 1 3 " ? # "

7 "

4 8 8 " " " "

# 1 : " " " #

" A : :

" * # " " " $ # " 1#

&- " " 0'(B 00&; " " " :

" # 9 $ # # ( "

&' " <

* " " " " "

# : 1 8 +

" $ " " * " " :

$ " " 8 * " 8 * . 1

7 " : " 8 "

" # : " " 1 #

* " 8 7 " : " "

# : *5 " 8 ! $ # "

" " " " " " : 1 " "

$ " , ) " " " , , " 1 *

, * 1

" * " * ! : 8 " " C " # :

" " 1 # * + " *

"5 $ ; * " $

8 $ " 8 $ " " 9+

: " " # " 1

(6)

(

8 " " + ; 1 8 + 8 :

# " " " , "

, ; $ " : " * "5

, : 1 : "

" " " # * "

* " " " $ 8

$ " " 8 * "

" " + " 1 8

$ # ) * : $ #

> * " * ; $ : 8 $

* " "

" " " 8 " "

# # " * " : " 1

* : > 5 # 8 "

" 1 " " : $ " 5$ 1 *

# 1 "

# # # 1

! 1 # * 5 1 " * *

8 " 1 : " 1 7 " " :

*> 8 1 * $ * $ " " + $ #

* : " 1 " + " : 8

: " 8 5

" 1 " 1 " + " 8 "

# 1 7 " # >* " + # *

" " 7 , * $

" + $ # ; * : * # 1

7 " # >* $ " " " " C $ " 1

1 $ " 8 8 * $

$ , " " >* " 1 7 " " 1

7 " " 9 " #

# " " " : 9

* 8 " " 1 ⁽ 1 7 " " " ; 5 , *

, $ # # 1 " 8

" "

) * 5 5 " 8 " * +" "

" " " 9

" # ,B * D < 000= . : 9 : # "

" : + " " . 1

$ " 4 8 7 " " " : 1 # 8 "

* * 8 * "

( 4 8 * >* " " : " :

>*

(7)

%

$ " " " " 1

, 8 9 1 + + "

" # 1 7 " # " . " "

8 7 " # : : # 1

" # " $ " : " " "

" " " >* 4 *

$ * + " " : * " "

" " ; " : * " " #

"

" $ " " " #

# " * " : 9 " " 8 *

" # " " " ^%$

" " " # : 8 7

" " , # " + : *

: " : " " * 8 #

: 9 " 8 "

# ( " " " * "

1 " 7 " # 5 $ " # % *

# " . : 1 , " # "

" " " .

" * " 1 8 " . " " " $

# " : # $ :

" # & * 8 " 8

" # " "

* : " # & ,

" 8 * $ " " 8 "

" " * " "

# - , 5 " "

" # 8 " : "

. A " " %

* " *

# " " " 1 " # 8

7 " #

.' # # ! # " / # ($ ( # $ #

" * # 1 " " "

# " 79 " "

" # 1 7 " # " $ # " "

" 5 " : " : " $ 8 " 5 1

" . " # 8 " " *

% # " " 8 * " " " # :

C& ' ( ) * + , ) - + . ! ) / 1,

0# ) $

(8)

&

+ " # , "

8 # " " " "

" " 1 7 " :

" "

" # 1 7 " # " " " :

$ " : 8 * " 1 7 "

1 8 " 8 " ,

" < =

.'&' # # ! #

" 8 * 8 " # 1

7 " # $ " " 1 $ $ "

" " C " " # : " 7 " # 8

" " 1 " # 1 " " < =

" # $ " " " " " "

C 1 * 9 $ " .

$ " " 1 " > 8 5 " , +

" " : . "5 $ # # 1

7 " * * " # 8

$ " $ " " : . $ " 1: " " :

" 5 " 1 " " 8 * 5

$ " * + " , #

. " : $ " " : # :

" " " " # 7 $ # >

9+ 8 " , 5 + ^& " 1 * * " :

* 5 . " $ 9+ 9 " :

5 " 7 8

" 5 : " * 1 "

" " $ " " * $+ " $+

" 5 " " 5 " 1 1

"> 1 " 8 5 " " " " #

> " " 9+ 8 " *

9 $ # 7 " " #

: : " +

7 " " 8 8 " *> : " 8 8 " ,

# " 7 " 1

" ) 1 2= $

" 5 * 7 $ 9 # " 5$ 1

" " # " + 1 " " #

" " " # ) # :

< =$

&

4 8 " * $ 5 $ " " 5$ " *

(9)

-

# " " " " "

: " ,

# " " " : " *

" " 9+ 1 " :

# # : "

, : + : 8 "

" + " " " " "

7 " : " " : " " #

, " " " )

* : # $ " " 8 8

" : * 1 8 8 8 , #

" * : " : " $ " , $ "

# + "

" 8 "

" 5 * $ " " * "

, $ " 8 " ! " *

" $ " " " $ " 1 :

" " " * 8 "

* 9 " " 8 " "

" * : 8 " 9

" " 1 +

7 " " " : 5 * >

9+ B? # " 9 * 5 8 " " 8 " 9 ,

" 9+ " . 8

9+ " " " : #

8 * , <& /

" , 0&- E 9 4 4 " $ )" " D 9F 1

G$$ H " 7 # 8 " >

"5 9+ <3 -=C



 



=

# %

4

7 # " : " " : $ >

" 8 5 . 8 " 9+ " #

: 9+ " : " 0 " 1 "

: 8 " . 8 (:( "5 "

4 + : # 57 & "

" ( #

" " " . $ * "

8 " 8 # " " "

" " ? # " , 1 > " :

" " " 8 "5

+

< =

(10)

'

" A " # "

<56 (57 2= 7 # " "

" " " , 9 * " # $ "

, " ? # " + #

" " " ? # " .

" 9 " . " 4 " 9 1 8 . "

:&I " " #

7 # $ " A " "

" " " " I " " #

" . 1 :-I " " . " 8 8

# & . " " " 8 "

" " " # " ^-

4 5 " : 7 " # " 8 5

1 " " # " " ,

$ " < =

: " 8 " " 7 " # #

" 8 $ " " C : *

(& . : 1 9+ : " 7 " #

'&I " " # < =

. " " " 7 " # # " ">

" 3I " 5 " " "

8 "> " -%:3I " " * 1 " :

&-I * * : -I

" " $ " " 1: $ " : 3I

" # <8 & # -

" # 1 7 " # " 5 " "

" " + : " #

+ : 5 " 5 " * " : #

5 " : " # 1 # #

$ " * " " : : 5 "

: " 8 , # 8 "

" 4 +: : " + ,

# > " 8 " J "

.'.' # # ! (#( "

" " " " :

" " " , : 1 8 "

" C " : " " " 1 "

" 9+ : 8 " " * " * :

" " 1 # 9+ " 8 " "

" " " : " " 1

-) " ,

(11)

3

" " 5 " , " :

: 1 " 1 " ^'

*" " " " " : # " 5 " 8

" 8 " " , # " " : 5

" ³ 8 " $ " : 8

+ " " : 8 5 " $ # " " "

" "

" , 8 " "5

" $ " : : " + " " + 1

" : # "5 " " *

" " * # " #

+ : : : ? # " 9 : 1 #

8 > 9+ ? # "

# * " 8 1 #

" + 4 8 " #

" : 8 5 , " , "

" 1 # " *" $

# 8 > 9+ 8 " $

" 9 + $ # " + " " " $

* # : 8 " " 1

, " #

" + " + " 5 " * " $ 7 # "

# " # " 1

#

" " 5 " * $ $ 57 57

9+ 8 , " " 9 , 8 , "

# # + 5 8

$ # 1

4 " # " 1 $ # *

" * 7 # " 5" 8 $ " $ #

" + " + 1 # " " "

" # < = 7 " " " $ #

* : + : 8: 8 " " + " " 1

$ # 9+ : 9 K " 5 " " "

" 8 " : #)8 9 : 8 " + "

+ " * " # : 1

" < L " : 0-3= : :

" + $ " " " : 5 "

'6 . : G 4: 00

3M " " " 7"

(12)

0

" "

" # : : : * " : 5

# < (= # " 8 #

" 1 8 7 "

8 * " : #)8 9 : 5 # "

" > "

" " 8 " 1 7" 8

* "

#)8 9 : 9 ; #)8 9 < 9 #)8 9 : 9

" # # "

$ " " 8 " " : 8 "

7 # < (= 1 # " " " # "

) * " " #

# " * " : 8

" " " " " : 8

, 5 " # $ # * "

" ,

( .'&' # ($ ( $ # # ( $

# ! $ # ! ⁺ ^#

0 " #

" #

" "

G* 1 7

) . , # " 1 9 , "

! #

B?

6 9B?

" "

,

"

$ " ,

B?

6 9B?

7 " #

4 " #

! " : $ 1

" #

" 1 " #

B?

6 9B?

G" " "

" * "

B?

6 9B?

4 "

" " 9+

B?

6 9B?

2 " " ),$ $ ; 4 $

)= >1 ; 1 % # $

) # ; # # # $

9 9 8

# 9 8

#< : == < : =⋅

< (=

< =

(13)

: $ # " " "

" # : 8 7 " > 9+ B

? # " 1 > B? # " 8 9 . "

: 8 7 " > "5 B? # " 1

> 9+ B? # " " 1

# # : 8 5 " > 9+ B

? # " 1 > B? # " 8 " , + < =

1' "# # $ $ #"% "* " / # ($ ( # $ #

" " # $ " " *

" + " 1 "

# " " " * $

$ : " * " * 1 " : +

8 " "

* " 5 $ # 8 "

" " , " # "

" " # * " " "

$ " " 1 " " " " $

* 8 " , # 1 # " "

* " : : " " " 1 "

5 " " " * " " " "

8 $ # * * " : 8 8 " #

" "

) 7" 1 * $ # : $

8 " >* : 8 " * "

# : " # $ " : 8

" , 5 " " # 7 " #

: " , 5 7 " #

$ " * " <, * $

* " * $ # 8

" " # 5 *

$ # 8 " 8 " #

" " * 8 " #

, " " # , " *

" : : 8 $ # +

$ " : " " 8

" * " 1N # 5 " "

" " $ " " 1 8 :

" " : " $ "

8 " * 5 $ " " " : "

" " # 1 7 " # " 1 # *

(14)

" $ " * * 8

" #

4 8 7 " " , # "

+ " # " : * :

" : " " * 8 #

: 9 " "+ "

" : " " %

8 "

1: " " : " 7 " # 5 $ "

1'&' $ #" # ) # # ! 2 " -

# " + # " # :

7 " # 1 " " " " : :

" " " 1 8 " " " " " 8 "

: " " # 7 " #

# ) 8 $ " 8 " "

" * * : " "

" + " $ " 8 " +

" " 9 " , 1 "

" " O B 5 * : " " 1 & D +

# " " " " " " *

$ : " " 1 " $ " " * :

, * 8 4 " # : " " 1 "

$ " " 9 " : : 9

1 " "> # : " # : " "

) " B 4 : ) " B : ) " B 6 P 9 5 <' ?>

@ $

) * : 8 " " # "

" : * 5 " * " " , #

: 8 " " , * $ #

$ # " : $ " * 5 #

8 " * # $ " 1 " :

* , " * # 1

" $ "

# <( = " " <=78=: " : 8 5

7 " # # " " " * "

< = 8 $ 5 " + 9+ 8 =78

7 " : 8 " , 5 * $ 8 "

" " 8 $ 5

" 5$ 8 5 + <9 = " "

$ 5 " 8 K "

8 5 " * # $ " " 8

(15)

" C 7 " " " : 9 " " " , "

8 " , " 1 # 8 "

, " 8 "5 , : 8 " 5 #

C

Q * " 9+ " "

9 Q 9+ " " "

Q " " # "

"Q " " " "

Q " " # "

! Q " $ "

/ " : " 8 5 " #

1 " "5 7 " # : 1 " " : 5 : "

" " < =: " # < = ) " #

" " : " " 1 " , 8 5 $ " :

" " , " $

+ 1 " "5 $ " : 9 1 8 "

" , 8 " * " "

# " " ,# 8 " "

$ , " 1 "

* $

) # "5 $ "+ : 7 " +

8 $ * " : " * $

" " : + 1 " " K "

5 1 8 " ) * :

"+ "

5 1

$ * " " " " 8

* $ " # K " " " " " "

" 8 5 , $ $ " "

# # ) * : , " # $ #

# ( . " " * 1

" " * " " $ "

" $ " *

$ # # * " * " *

" " K " " 5 9 $ "

8 " " # $ " 1 " 1 8

1 " # " 8 " #

" " # " " # "

∑ + + +

∑ −

∑ ∑ − +

= +

=

= =

1 9 9 9 !

=78 < < = < = =< =

=

<

=

=<

<

<( =

(16)

(

" " "

# " " #

" * 8 " # " *

" + " 1 " "

" / "$ : 9+ + : <5,0 ,0 *=

" " " #

" 5 " " # " :

$ " " 5 D + : " 5$

,# # " " # : 9+

)5,0 ,0 *= # " 5$ + / F 1

" 6 : " : 8 " " + " (%

9+ . $ " 8 # # &

" $ 1# $ " " . : 1 8

:'& R "# 9 " ( 9+

< 3 *=

* " * # :

" " : " 8 " " " 7

" 8 7 " " " " #

" " # : 8 " " *

$ # 4 +: 8 5

$ " # 1 7 " # 8 :

5 " " # * 8

" " " " * $ " # :

7 " # " 9 . ' ?>A B ? 5

) C A 1 7

/ $ " 1 * " "

: "+ * 8

7 " $ 1 " " $ "

#

( : " " "+ " # "

" " # 1 1 8 8 5

$ , # " " " * : *

# " 5$ : 1 # "

7 8 " * # $ 8

# " " # :

8 7 " # $ " " " "

) * " , $ " "

: 7 " 5 " # $ "

1 + # 7 " #

" K " * 5 .

$ " " : " 8 # "

"

(17)

%

( 1'&' $ "# # , 2 " , # #

$ "# , 2 # $"% $")" !

#

7# 3# >(# #4

) _{" ,} _*

4 " " " 5$

#

" + " "

( , 5

5 )

* " ,

$ " *

' I

"

) " 5$ * "

"

( I

# 753

)

* " ,

$ " *

' I

"

) " & I

" " " 5$

" " 8

" , "

* " " &I

A " C 3 ) * ' ?>@ )

" # $ " " #

$ # " "

# " " * " " " " :

* 8 7 " " * $ 8 5

1 " 1 8 " + " , # 8 *

*

# 8 : :

" 9 "

" " : 7 " " " $ " "

" " " 1 " # " " *

# " : # "+ 5

* * # " " :

# : * : 5 1

# " $ " 7 " #

1'.' 0 ) # ! 2 " ! 3 $ $ #"%

" " : " " , " #

* " " " " #

8 $ , # , 5 " " " 9

* 7 # "

7 B " + " * * " 7

: " 8 " 9 * " " <5,0 ,0 *= )

" " " " ? # " :

# ( ( # # " # 8

(18)

&

8 $ # , 7 " # # 5 * 4 8

" " " + # & . : " " " 7" #

.

6 " $ 1 $ " 7 <0# -=

7 " " , " $

, $ "

* " " : " "

$ 8 " " : " & 1 . K "

# " # 8 * " 1 8 +

# $ " " $ : 1 8 ,

* " 7 " " : 1 8 $

" $ " : 8 # " >* " " :

8 8 " + " " K "

8 " * " " + " #

1 " " >*

" " : * " 8 9 *+ " *

# <( = " , : " * : 7 =78

# 8 " " " " " 8

" + : $ "5 " " # "

" : " $ + <

+ # # # 8 "

: 8 " " " # : 1

7 " # < " " : " # 1 $ = 1 8 $ "

# "

/ 8 " + : "

" " " 1 $

+ 8 " : 1 8 5 "

7 " # 1 " 5 " " * $

"+ " * * 7" # # " "

+ K " " $ " ,

7" # , # # " "

"+ " " "

# 8 " " " , : * * :

" * " + : 8 " " 8

8 8 " # " 5$ 5 " " 1

" 5 $ "

" $ 7 * " * " * " " " " $

8 " $ $ " "

8 + # " " ) " "

" 8 " " " " #

8 : : $ " " " : 7 "

# 7 " , # 8 * * 8

, # " "

(19)

-

1'1' 0 ! 2 " - # )

$ # " " * " "

8 , " $ # >

9+ 8 " , + 4 * " " :

" 1 7 " " " # 1 $ "

# " " "

4 $ " " " # " :

, > " " + : " " :

" 7 " " $ , *

# $ " 8 " * # *

$ # > 9+ 8 " , + " " : > $

" + 8 " *"

" >* *" " "

# " " " " " " : 9

" " # # "

" 1 &I " : " "

$ " * " I 7 "

" " # $ " " <

" " 9 " " * "5

" # : " " 1 7 " # " 9 1 "

" 8 " " &3 ? # " : " " *

" ' ? # " 8 * S 1 9"

A : " # "> 2 8 + 7 # "

"" 1 9 4 " : : 5

"> : * * 9

" # 8 * " " " #

$ " " 1 8 "5 $ # > 9+ 8 " , +

< $ ( * "

8 " "

( ( " # " "

1 " 5$ * * 7 "

* 8 " * " 5$ "

*

" " # : : $ * " "

: ,# 8 # ,# "

" # " " C "

* >" 1 " " " .

: " " 8 *+

" ; 1 $ " * *

( ( # $ " #

" ,# 8 . * "

(20)

'

"+ 1 " " * " : + #

>" 1 "

( 1'.' 4 $ # /" $" # $ - # # ) ! " "

4 $ 5 6

7"!% # " *2

/ $ % "$

! $ $ #" "

8 "!! # !") #

# !" #9

"$$"% /"$" !

* ! #

" , # # 8 "!! #

!") # # !" #9

5 >7

D 1 ⁰⁰⁰ ^&

4 " " B 4 " + B&

( (%%

7 )5 7 # >

#

003 4 " " &% %

7E :7E -

& >

' #

003 & " B

(

7* >

8 ^00' ^{3% (}

"

- &'

A " C ! , ( 0 ) /

( 1'1' / - # # ) ) # /"$

:2$(! # # # :2$(! # !", #

"* ! /"$

:; 5

8 "!! #9

-

* :<7

8 "=( #9

, ( !

8 "!! # !") #9

:; 5

8 "!! #9

-

* :<7

8 "=( #9

, ( !

8 "!! # !") #9

3 B' 0 - ( B( ( 0

3 2 ' B - 3 ( B%& (

3 C B ( ( 0 %& B&&

3 E 5 ( 5 &&

2 " " = >1 ; % # >1 $

A " " ! , ( 0 ) /

: # " " 8 "5 "

>* 1 " " : "

8 " * # 7 " # " : ,

" 8 7 " # + " " "

" " " " " * #

" " : 9 1 "+ 8

" * 5 $ "

(21)

3

" # " 9 " 8 *

" 7 " # " : "

9 " : # " " " * "

> " "+ " 5$ 9 "

" : " " : " " " " ,#

8 $ $+ "

" # : " " : $ #

$ " " : 5 8 " # 1 " " +

7 # <( = " 7 " " 1 "+ $ " 8 *

, " , * <=,7 &=

" >" # < = *

7 " " , $ " 8

5 # 1 7 " # $ " " 4 $

" " : * "

+ : " " : * # 8 9+ B? # "

*+ " 9+ " $ 5

$ : # 5 $ " " 9+ 1

# : " * "

" * 8 "

" # 1 7 " # "

" * 7 " # $ " : " " "

" # 7 " # $ " " , #

" : " " " : " 5 " * $

" , + : " 5 " + 1

" " 8 " 5 " 1 " "

* $ / $ " " #

" " 1 " : 1

9 " 1 " " * #

) * : 7 " " $ " " :

" " : " 8 57

# "5 " " : " " 1 "

9 * " # 1 + * : > " " 1

" : "

" " " " : # " "

8 " 8 " * " "

# " ( *

" * : " & . $ # : " 9 "

% I * " % I "

" # " * $ : *

" 5 $ 9 $ "

" , $ # 1 "

<( =

( )

1 99 9 9 !

=,7 &

=

=<

=

<

= <

<

=

=<

=

<

< +

∑ +∑ + +

∑ + + =

= ∑

= = = =

(22)

0

# " " .# " "

" # " * 4 8 *

8 $ " # $ " : 8

" * # " " * " " " " " $ " : + "

+" " " * 1 " " " 1 :

: 5 " 5 " .

$ " #

# " " " " "

# " " $ # " "

" " * # #

8 * * <A8 =: 8 " 1 , : * 8

7 " # 7 " " * " "

# " $ $

8 # # 1 " "

<A= *" 9 " " #

" " < =

7 # " # 8 +

" , 7 # " " < =: > #

<( %=

) * : 9 1 " " 8 " * * " "

: # " " :

# " # ⁰ # " "

7 " 9 " " " 1 " #

8 " 5 8 " 9 " 5 1

" " 5 " " # " "

7 " # 5 7 " : " * : 9

" $ : 8 " 7 "

" * " 8 "

* " " * # " 8 " *

" $ , " " " " 5 5 " 5

" " " * $ , # " "

" " " # " 8 * + *

8 + > " # <( &=

0 " " # " 9 ) " B6 + B6 . < "

G* >* : 033= " , * * 9 " " "

<( (=



 



 ∑

− +

= =

=,7 & A

A8 < =

<( &=

<( %=

( ) ^^









∑

= + −

+

− +

 +











 ∑

= +

−

= A !

=, &

A8 _& < =

=

<

=, & A

A8 < =

=

<  +



 



 ∑

− +

= =

(23)

# " " 8 $ , " " $ #

9 " * ,

9+ 1 * " 5$ 4 5 " " +

* > " 1 " * " * "

" " # " 5$ " " "

" * 5 " " 5$ 8

" " " " " 5$ *" " " *

, " " *

# " 5$ " # $ # " 9 "# 1

" " $ # " $ $ #

* 5 " * * " " : " :

$ " " : " " " 1 "+

+ " * " "

" 8 57 * < =

" # 8 1 "

" # : " " 1 " #

1'>' 0 ! 2 " * ! # ! # " , # #

* 8 " # "

" * # 1 9

: " 9 # "+ .

+$ " , $

" " + "

9 9 $ " " * " * #

: , $ "

" # 8

1 "

" " : $ " " : " " " *

$ 7 + " # # : 8 $ ,

, $ $ " " # * "

8 $ # 1 " * #

# " " $ " : 8 :

, ) * : :

# 9 " 8 , $

8 "#

" " $ " " # "

) " B6 + B6 . 1 8 " $ " " :

" : " # "+ 8

* 9 1 9 *+ " , $ " #

* 8

, " 5 8 "

# " " - 1 -&I:

( I: <, * $

(24)

/ * 8 * " # 1

7 " # : 7 " " " " #

$ " " 7 <, * $

" " " " " " $ "

" " " # : " 7 " #

" ,# 8 " " # :

" " 1 7 " # : $ * $ 5 57

"

" " , ' ), *

" " " # , $ 9 #

# ) " B6 + B6 . 9 ) " " 1 " 8

" # " "> 1 9 * " # ( ? # "

" + 8 ) " " : # -

9+ N + . 00- * 8 # "

$ " (% # " , 1 $

003 < , 7 " # . =

. : ) 1 : $ " " , (3 #

# # " " & . #

# <' ?>@ $

" $ " <5= A= * *

" " , # : 5 "

" " 1 " # $ " " 1 $ " " $

8 $ #

4 $ " " # " 1 * 8 ,

# * : " " " , " $ :

" " 1 " # 5 " #

# < =

# : 1 " " $

7 " # $ " " : 5 # : 8 $

* : " * " : 8 $ 5:

5 # 8 " , " : 7 "

" " "

" " : 1 8 7"

# 8 9 * " # 1 " "

$ " " : 8 " " " " 1 " #

: 1 " " " * #

" " : 5 , " 8 " "

" * # # ) * " " 5

" # : " *

" * 57 8 5 *" 8 1 " " 7 "

<, *=

<( -=

( )

1 9 9 9 !

5= A < < = =< =

=

= <

< +

∑ +∑ + +

∑ +

=

= ∑

= = = =

(25)

" " # " # : + 8

" " : * : 8

" " $ $ #

+" # 8 " " 8

# : 1 8 # * *

" 7" # # #

7" # # * : 5 "

" " " 1 7 " # + * !

* : +" 8 "

: : " # " " #

" " 5$ : 5 $ " " : # ,

# : " * 9 " " " 1 7 " #

( % " " " $ 8 .# # ) " B

6 + B6 . 1 # * " . 1 " , #

$ " + ( & " $ #

" 1 " * " #

" " " " * " * " " " $ " $

" $ " " # " ) " : " " :

" " " $ " 8 : 5 $ #

8 " 8 " $ * "

" " # 1 5 " 8 + *

# " " 5 "

# # 5 5 8 8

" <, *=

( 1'>' $ # $ * #"% ! "/ " # ( !

$ $ #"% " , < ! 2# < "5 !

$ $ * #"% * :2$(!

" * :2$(!

! , # "% ! $ , # "%

5 # !# (

7# # (

( ( &

A " " 5 6 # ) / $

(26)

(

( 1' ?' " # ( ! $ $ #"% " , < ! 2# < "5 !

"* ! $ , # "% " " ! 5 2 # @ "

7 " B " 4 " 1 A) / T

U " + A) 0 B (

" P " 4 " 1 A) / T

U " + A) ' B 0

" P " " / ' B

G " B " 4 " 1 A) 6 T

/+ " A) 3 B

G " B " 4 " 1 A) )5* T

+ A) B %

8 ⁸ ⁹ ^{" # 1} ^" ^{" #}

2 " "<A) =; $

A " C5 6 # ) / $

. +" " $ " 5 " 1: " 9

" # # : " " 8 " "

" 8 * *

# 8 " " 8 * 5

1: : # # #

" * #

7" 7 " < , # " " . =:

8 " $ " " # 8 "

" , 8 ' ?>@ ) =: "

8 9 " 8 $ " >*

9 < " 2 " = 9 1 8 "

" + " " , " #

" " # 8 9 " " " , $ "

" " " " " "

#

+ " " 8 $ " $ #

" " # " * *

: " 8 " " " #

$ " " " * "

+ " ,# 8 " $ "

# 8 ,# # 1

"5 " " *"

" 7 " # : *" # # 8

* * $ "

$ " > !! " , # " 1

" # + , *

" $ # : " " * " 5" :

> * * : #

(27)

%

# " " " #

* 1: $ " : " "

+ " 5 8 +

" , " " : " # "

" " " " " : 8 " 5 7 ,

" " " $ " " 8

# 8 * " + " " ,# "5

8 " 5 # $ 1 7" #

# # 9 9 " # #

+ 1 " " " : " # 1 $ 1:

" " : * $

" " $ # <(

- $ 4 $ " 8 " "

" 9 1 8 : " " : 5

" " # "

8 * "

" "

# " " 8 "

" " * " " "

, $ : 8 $ " $ " :

8 " " 8 " 1 "

# " " " * 8

" # " " )( - $ : $ "

# $ " # " 9 ,

# $ " " " " 8

# 5 " " .

$ " # 1 * $ 8 8 9 "

1 # # $ # # : "

" " 1 # " $ 8

$ # 1 "

" : $ " " " " 8

7" , # : " 8 "

* : 5 8 # " # *

<, * $ # +"

, # : " 5

" # " " 8 #

* " # # ) " B6 + B6 . " * +

* 8 # "

" $ " , # : 8 * 9 *+ $

:&I 1 8 %I 1 " -:&I:

* * " * $ # " "

(28)

&

8 + " * " %I )5 6

/ $ $ " "# " $

( - " + "

" " , " , "

#

(29)

-

( 1'A' # # $ $ #" # "* # " / # ($ ( # $ #

B(, < (!(

8 ! )" 9

( /

8 " " 9

0+"$ < !($

8 0+"$ 9

&< & 7#:"

8 " " 9

" , < ! 2# <

"5 ! 8 :"! 9

5F # ⁺

"+ 6 " + # + * + "

7 # ^{9 * "} ^# ^#

"

2 " # % 9 * " # 1

# " 9 * " # 1

#

9 * " # 1

" # ">

( % 4 " " " * # 4 " + * 4 " + " * 4 " " ! " *

#

) G ⁽ ^- ^{( (} ^%

8 1 ( - ( &

4!

) % # : % ^-

1 )G %3

#

) B ^&

* 8

- & # ( 6 * : 57 &

2 " " $ $ ;

(30)

'

>' # ( "# # - # 5

" . " " " " " + C "

: 1 " " 4 " # " : "

: 8 " " 4 "# 1 "

" " * / " " $ 9 1

8 " " " " : " + 1 " " * : "

* , 1 " " < % = . 00' - '0&

? # " " 8 : 3 '% "

1 " -( " " ( ? # "

" 4 "# : " "

4 " # "

" " " " 1 $ # 1

" " # " # 1 " " 1

7 " # # " "

. : * 8 " # >* 0I / "

" # " 8 &3I "

" " : 9 :

" " 1 * ; (I " " 8 . "

" # 7" " 'I " )5 -

" # " # " " " #

" # : # 1 7 " # " "

9 " # >* 1 )

* " : , * * $

# >* 1: " : 8 +

"

) * : / " ( N 03% " ,# # )

E 2 4 " " : ) 4H < 24 )4=: " $ 5 #

8 + " " 8 1

" # 1 +" " " " * " " C # +

" " >*

" : 1 * " " # 7 " #

9 + : 1 " # " 8 " " * " 1

" " " " >* "

" " " # "

4 : " # " ) " # 8

" " 4 4 )4 1 & I

4 / 24)4: " " * $ *

" " 4 /4)4 1 ) 4 " " 1

4 " + : ) 4 " " : $ # " "

4 " " 1 > "

24 )4

(31)

3

( >'&' "# ")($"% ! $ #' &CCD' ," ( 7"!% #

" "# $"% ! ( " # ( % #

" ( $" #

4 )"! #

( 2 # ⁽ ^{"# #}

-

( "# #

!") # 4 ( *2 #

# )!

$ !3

#

$ # ( "# #

-

( "# #

!") # 4 ( *2 #

# )!

$ !3

#

$ #

# ! #

$ #

!

7 # % 0( 0 0 0%' %'( '& 0 3'- % -3&

7 ^&3 ³ ^-' ^'%3 ^- ^{& (00} &&(

7 # ⁰ ^&(' ⁽ ^{% 3(} ^{% ''%}

3 &3 ' (' '&' 0%

'& &- '%0 (%- % ( -

0 % ' (( &3

>@ 5 ^'33 ⁰ ^{& -} ^{' 33-} ^{' '} ^{3 %3}

@ 0% && ( ' - (0 & &- - '3( ( &&-

#B ^%- ^' ^3& ^0- ^-- ^%& ^%& & 3& % &3 0(-

,H # ⁽³ ⁰ ^' ⁰ ^{( %'0} ^{( 0&0} ^{3 '3-}

' -- ' &' &' (( % & 3& 0 33 ' -3

5 ' %& & ' &- &0 ( (&3

5# ⁰ ^(% ⁽ ^'% ⁰ ^{( &'}

8 ⁽⁰ ^'( ^{( &%} ^{( '--}

% = 0- % % (0 % ((0

0 ⁰ ³ ³ ³ ^('- ^'0&

= ^3' ^%-- ^%' ^% ^&& ^{' (} ^{( 3 '} ^{3 % 0}

# 5 & (& -

&'D?. >'>DA AC& &A'>DE 1&& &'F1E >D. DF'A.1 AA'C?> &A.'DC?

A " C5 * -

(32)

0

$ " " " "5 " " " #

*5 8 " . " "

# " , @ /: -2 #

H # F )I ! # , -2 1

@ C: * 9# ! % # 2 / C 2J CK @ /: -2 )I ! #

, * 1 @ **: - 9# ! % # 2 / 2J @

/: -2 # @ C: * )I ! # , - $

/ # * ) 4 " "

2 # 4 " #

" : > $ 0

*J-: /* ? !# '

& 7# 8 )

' /* $ ) " " # " " " "

G* >* 1 * < " " A " = " "

$ " A " * # :

: " $ 1 " *

8 " *

" " "

# " " * # O "+

G$ " <OG = * 1 5 " "

" 8 * 5 " # " " " #

+$ #

>'&' #$ " $"% ! #"# ( "# # - # 5

) > "+ @ /: -21 " $ <@ C: *

@ **: -=: L 4 # # !%

# % H 9# $$$M

, : " "5 * " "

# . $ " : 1 7 "

" " 2 : " " : 7 " " *

" # " 7"

% " + "

" . ) " " 8

- . : " "

: 1 # : 8 & . 1 +

) " " " " # 8 " #

< " 4 "# = 1: > " : "

* 8 " " 0I < % = 5 " >* 1

" " 7 " I ? # " " "

" $ " " >*

(33)

(

( >'.' $ 2# "$ # ! # # $" # $ $ #" " #' &CCE

$"

$ #" "

" " ," (

87 9

" $ $ #"%

8 G 5 #9

" "# $"%

$ $

:2$(! #<7 8 "!! #9

" ! # $" ! 8 "!!' #H 1&<&.<CD9

"

7 ,&7 4B V , " 5

4B' B 1

4B' S 8 B

4B ' O B " #

4B 0 " "B $

&% :& 0-'B - <%0= "

" " " .

- %((: '

7N 7@&7 4B-- # 3': 0'&B <%-= " %':0 & 3% >*

7N 7( 4B - O B B &': 030B (0 <& = " " " . &': '3(

7N 7&7 4B0 A B A "

"

-:% 0'(B ( <& = " 3& : ( &00 >*

7N ,87&7 4B & B! , : 0'(B 0 <&-= / " # A

* 2

( 3:3 ' ' >*

7N570 4B' B6

4B' 6 B4 "

4B% ) B 5 ,

&:(

%3:&

0(:3

0' B 0 <%3= " & :' -- ' &

7N(,57 4B 3N B0 ) "B %3:( 03-B (- <& = " " " . &3:' ( - -

7# 4B&& 4 . B *

7 B6 .

( :- ':(

00&B %& <& = W " % %%( >*

7# & 5 B " 3 : 00-B %- <& = " 00

7=7&7 4B-3 O * BV , 0%: 0'(B <(3= " '0 : %&

,# 4B3 O * BO 9 * -: 0-3B ( <(&= " '% : &3 %'3

,# % 4B O B4 .# 3%: 0'(B ' <%%= " ('&: ' 33%

A 4B- 6 * B4 -0:- 0-3B 3 <& = " %'%:' & -% :0

(737&7 B0 > 6 ': 03'B (' <& = " " " . ': - 7"

( % B0N B % > + ( : 0'(B ( <& = " " " . %':0 ' &3% 7"

( & B' > )# (: 033B - < 3= O &:' ''

A " C7&,(7 ) /

(34)

(

% ( " # " " "

> " . : 8 -( ? # " 00' / " "

" " " " : " " "

. 00 1 00' : &I: > " . "

" :(I " > " . : " " * " 5

" " + 1 " " * : 8 $ %:&I:

" 8 " + " " "

# *

( >'1' # , $ $"

$ # &CCF &CC1 &CC> &CC? &CCA &CCD I CA<CD^&

7# ² 303 00 ( ' -( :(

7# % # &(' % &3- % %'% % 0(0 & '- & & % %:&

? -0 3 ' & ' % -( B(:%

?'&.A D'>F> D'D1A E'&11 E'>CD E'D>F .HE

= % # >1

) ^C

0 -: 0 & 0: 0 '3(: 0 '3 :' 0 &%%: (: -:

"

$ " . 00' < -( ? = % & < -( ? =:

" " 8 9 * " $ "

( > " " "

A " C5 ) * -

1 " " # 8 $ "

" 5$ * " " : $

" 5$ 9+ 1 9+ 1 C

" " : " 1 9+ $ ?

9+ : 8 " * 1 : "

7 " -I " " " 5$ . 00' "

" "

" " " " 9 " * " " $ 8

" * # " * " " 9+ 1 8

< " 8 9+ " * "

" " = 7 < = "

" " " " " $ #

7 " <! /= " * 8

" " " $ $ 1 * " * # " 5$ :

+ 9 1 $ " " $ 9+ 1

$ " " " " " , " " : 1 8 "

+ > 9+ < # =

(35)

(

< 3I= " 9+ "5

" " # # # " " "

$ 8 " 9+

8 * # #

" * " 5$ : 8 " "

8 " 1 # 9+ "

" : $ " " :

> +: " 9+ "> *

) * : " " " : * 8 $ 1 "

* 7 " " " " ) * 8

8 5 !* " : + 1 4 4 )4

" <! /= ,# 00' & 0%- 9+

" $ " " . "

7 " -I ) * : " * "

" " " " 7 " " " " <

7 =

* 9 1 8 . 8 " " 5$ + +

*" 9 " 1 C . 1 " "

/ 8 " -I 1 'I ! / " 9 "

+ 4 + : * # $ " 5$ :

" " $ " " "

+ 1 " " 5$ : ,

% I * ! / " " * "5 "

: 8 1 ) ) " "5

" 5$ " 5$ " "

*" " "

" " $ 8 * " 9

" 1 $ 5

< 7 = $ # " *"

" " " " " : 8 $

*" 7 " # " " 5 : " *

$ " " " 8

$ $ 8 7 " # " " "

$ # : 8 "

8 " "

" " "

" " : " " 7 " #

7 " (I " " ( < 7 = "

$ # 1 "

. 00' % < 7 = " $ # " " "

" . . 00- # "

" 7 " # 1 " $ "> " :0I

4 )4: 8 " " * 5 7" : 1 :' I 4 4 1

" (I " " ? # " " .

(36)

((

>'.' ! # ! #"# $ $ #"% # 5

9 " # $ #

1 " 8 8 * 4 " # "

$ # >* : * # 5 1 *

" , " , " # "

# $ " * " " " "

# 1 " " $ " " " 5

" # $ " " ) # "

: : $ " 8 8 " " :

" $ # $ 8 $ " 8

8 " " + " * " "

" #

, " * $ # $

" " # 5 " " 8

* " : 1 "

% % " " # # " "

4 " B " * # " "

$ + " 57 " : 5 #

8 $ , " 8 : " "

# : " $ "

$ # "+ ( @ /: -2 @ C: * " * 8

, # " " # : 8 " , :

1 * "+ & * @

C: *: '& . * #

" " $ + " 57 " :

5 # 8 $ , " 8 :

" " # : " $ "

( >'>' " " # # ! $$"% ! -( "$ $"% ( "# !"$ < ,

" " # ( ( $"%

6 1 " , " " " " "

" " " " 1 + " 57

* " 4 " # " "

" $ 1 " " " "

" " "

( / * " $ : " 1 9

% 9 1 # BA

& " " " 5 " + " " " 1

$ : "

(&

&

A " C5 ) /

% & " " $ 57 " *

5 " " # 4 " B : "